New pc build, need some psu help

I have yet to see a psu of adequate power that does not include all the power leads you might want in a normal build.

GTX1050 or most GTX1050ti will run on slot power only.
You are good.
So long as your psu behaves itself, I would not change it out.
It should be capable of running a card as good as a GTX1070.
Here is a good chart for other options:
http://www.realhardtechx.com/index_archivos/Page362.htm

Whenever you buy a new psu, try to buy tier 1 or 2 from a list such as this:
http://www.tomshardware.com/forum/id-2547993/psu-tier-list.html